An orthogonal basis for this inner product was defined in [1]} in terms of the Jacobi polynomials.
For \({\alpha }, {\beta }> -1\) , the Jacobi polynomials \(P_n^{({\alpha },{\beta })}\)  are defined by
\(P_n^{({\alpha },{\beta })}(t) = \frac{({\alpha }+1)_n}{n!} {}_2F_1 \left(\begin{matrix} -n, n+{\alpha }+{\beta }+1 \\{\alpha }+1 \end{matrix}; \frac{1-t}{2} \right),\) 
